Determination of the Relative Positions of Three Planes: Action Research

Bu calismanin amaci, ilkogretim Matematik ogretmen adaylarinin uzayda duzlemlerin analitik incelenmesi konusundaki basarisini arttirmak icin daha etkili bir ders planinin ve ogretim ortaminin nasil saglanacagini arastirmaktir. Bu amaca ulasabilmek icin arastirmacilarin hazirladigi plan dahilinde eylem arastirmasi yaklasimi kullanilmistir. Uygulamanin 1. asamasinda ogretmen adaylarina uc duzlemin denklemleri verilerek duzlemlerin birbirine gore konumlarinin belirlenmesi istenmistir. Bu asamada ogretmen adaylari duzlemlerin birbirine gore konumunu ikiser ikiser duzlem denklemlerini inceleyerek tek yonlu belirlemeye calismistir. Uygulamanin ikinci asamasinda uc bilinmeyenli uc denklemden olusan lineer denklem sistemlerinin cozumunu bulmalari ve bu cozumu geometrik olarak yorumlamalari istenmistir.  Bu asamada ise ogretmen adaylarinin bir kismi denklem sistemini cozdugu ancak geometrik olarak yorumlayamadigi gozlemlenmistir. Ucuncu asamada ise uc duzlemin birbirine gore konumunun gorsellestirmesi ve duzlem denklemlerini kullanarak bu duzlemlerin birbirlerine gore konumlarini gozlemleyebilmeleri icin bilgisayar cebir sistemlerinden Maple programi kullanilmistir. Bu asamada ogretmen adaylari duzlem denklemlerinin olusturdugu denklem sistemlerinin cozum kumesi ile Maple da elde edilen uc boyutlu gorselleri iliskilendirmislerdir. Uygulamadan elde edilen bulgulara gore hazirlanan planin matematik ogretmen adaylarinin uc duzlemin birbirine gore konumunun gorsellestirmesinde olumlu etkisi olmustur. Anahtar kelimeler:  Uzayda duzlemler, analitik geometri, Maple, eylem arastirmasi Determination of the Relative Positions of Three Planes:  Action Research Abstract The purpose of this study was to explore how a more effective lesson plan and teaching environment can be achieved so as to improve elementary mathematics teacher candidates ’  achievement in analytical examination of planes in space. In order to improve achievement in expressing the relative positions of three planes not only algebraically but also visually the study used an action research approach as planned by the researchers. In Implementation 1, the teacher candidates were given the equations of three planes and they were asked to determine the relative positions of the planes so that their prior knowledge could be identified. In this stage, the candidate teachers tried to determine the relative positions of the planes in one direction by examining the plane equations in pairs. In Implementation 2, the candidate teachers were asked to find the solution set of the linear equation system consisting of three equations with three unknowns and to come up with geometric interpretation of this solution. In this stage, some of the candidate teachers were able to solve the equation, but they couldn ’ t interpret it geometrically. In Implementation 3, Maple, a computer algebra system, was used so that the candidate teachers could visualize and observe the relative positions of the three planes by using the plane equations. In this stage, the candidate teachers associated the set of solutions of the plane equations with the three-dimensional images obtained with Maple. The  results of the implementation showed that the proposed plan improved the mathematics teacher candidates’ visualization of the relative positions of the three planes. Keywords: planes in space, analytic geometry, Maple, action research